quantity of water caught in this way, the differences and proportions of their weights gave the differences and proportions of the times; and this with such exactness that, as I said before, although the experiments were repeated again and again, they never differed in any degree worth noticing." In order to get rid of the friction, Galileo afterwards substituted experiments with the pendulum; but with all his care he erred very widely in his determination of the space through which a body would fall in 1´´, if the resistance of the air and all other impediments were removed. He fixed it at 4 _braccia_: Mersenne has engraved the length of the '_braccia_' used by Galileo, in his "Harmonie Universelle," from which it appears to be about 23½ English inches, so that Galileo's result is rather less than eight feet. Mersenne's own result from direct observation was thirteen feet: he also made experiments in St. Peter's at Rome, with a pendulum 325 feet long, the vibrations of which were made in 10´´; from this the fall in 1´´ might have been deduced rather more than sixteen feet, which is very close to the truth. From another letter also written in the early part of 1609, we learn that Galileo was then busied with examining the strength and resistance "of beams of different sizes and forms, and how much weaker they are in the middle than at the ends, and how much greater weight they can support laid along their whole length, than if sustained on a single point, and of what form they should be so as to be equally strong throughout." He was also speculating on the motion of projectiles, and had satisfied himself that their motion in a vertical direction is unaffected by their horizontal velocity; a conclusion which, combined with his other experiments, led him afterwards to determine the path of a projectile in a non-resisting medium to be parabolical. Tartalea is supposed to have been the first to remark that no bullet moves in a horizontal line; but his theory beyond this point was very erroneous, for he supposed the bullet's path through the air to be made up of an ascending and descending straight line, connected in the middle by a circular arc.